The kinetic energy k of an object in joules is given by the formula k=1/2mv² where m is the object's mass in kilograms and v is its velocity in meters per second. An object’s velocity is 20 meters per second, and its kinetic energy is 48,000 joules. If it speeds up to 40 meters per second, what is its new kinetic energy?

Each time x goes up by 3, y goes up by 2. The rate of change is constant.

slope = (change in y)/(change in x) = 2/3

y intercept = 6 since this is where x = 0

The equation of this line is y = (2/3)x+6

Answer:

Linear, The rate of change is constant.

Step-by-step explanation:

-3 + 3 = 0

0 + 3 = 3

So x is constant

4 + 2 = 6

6 + 2 =8

So y is constant

Answer:

I think it would be thirty

Answer:

Step-by-step explanation:

To get from - 3 degrees to 0 takes 3 degrees to do

To get from 0 degrees to 12 takes 12 degrees             Add

Total                                                   15 degrees.

Answer:

20 points

Step-by-step explanation:

If Jenny scored 3/5th of 50 points then:

Jenny = 3/5 × 50 = 30 points

If Hunter scored 1/5th of 50 points then:

Hunter = 1/5 × 50 = 10 points

Difference in points between Jenny and Hunter = 30 - 10 = 20 points

Answer:

23

Step-by-step explanation:

To get to 17 degrees, you need to add 6 to -6 to get to 0.

And to get to 17 from 0, you need to add 17.

So then you add 6 and 17 together.

6+17=23

Answer:

y = - [tex]\frac{2}{3}[/tex] x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 3y = 24 ( subtract 2x from both sides )

3y = - 2x + 24 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + 8 ← in slope- intercept form

The equation 2x+3y=24 in the slope-intercept form can be written as [tex]y = -\frac{2}{3}x+8[/tex]

From the question,

We are to write the given equation in the slope-intercept form

The slope-intercept form of an equation of straight line is written as

y = mx +c

To write the equation, 2x+3y=24, in the slope-intercept form, we will make y the subject of the equation

[tex]2x+3y=24[/tex]

First, subtract 2x from both sides of the equation

That is,

[tex]2x -2x +3y = 24 -2x[/tex]

This becomes

[tex]3y = 24 -2x[/tex]

Now, divide both sides by 3

[tex]\frac{3y}{3} =\frac{24-2x}{3}[/tex]

∴ [tex]y = \frac{24}{3}-\frac{2x}{3}[/tex]

[tex]y = 8-\frac{2}{3}x[/tex]

In the slope-intercept form, we get

[tex]y = -\frac{2}{3}x+8[/tex]

Hence, the equation 2x+3y=24 in the slope-intercept form can be written as [tex]y = -\frac{2}{3}x+8[/tex]

Learn more here: https://brainly.com/question/20076300

Answer:

Step-by-step explanation:

Simplify the following (12+7)-(2-23)

(12 + 7) - (2 - 23) =

19 - (-21) =

19 + 21 =

40

Answer: 3

Step-by-step explanation:

Answer:

i believe its 1200

Step-by-step explanation:

The sum of forty-five and a number n is 46.1, and the expression that can represent this can be written "45+n" where the value of n is 1.1

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The statement that is given to us is" the sum of forty-five and a number", therefore, the expression that will represent this can be written as,

45 + n,

Now, if the value of n is 1.1. Then the sum will be,

[tex]45+n\\\\=45+1.1\\\\=46.1[/tex]

Hence, the sum of forty-five and a number n is 46.1, and the expression that can represent this can be written "45+n" where the value of n is 1.1

Learn more about Expression:

https://brainly.com/question/13947055

Answer:

20 games

Step-by-step explanation:

Given

Customers:

[tex]Rent = \$5[/tex] per game

Members:

[tex]Membership = \$50[/tex]

[tex]Rent = \$2.50[/tex] per game

Required

Determine number of games for both to be equal

Represent the number of games with g

For regular customers;

g games cost: [tex]5 * g[/tex]

For Members

g games cost: [tex]50 + 2.50 * g[/tex]

Equate both expressions:

[tex]5 * g = 50 + 2.50 * g[/tex]

[tex]5g = 50 + 2.5 g[/tex]

Collect like terms

[tex]5g -2.5g= 50[/tex]

[tex]2.5g= 50[/tex]

Solve for g

[tex]g = 50/2.5[/tex]

[tex]g = 20[/tex]

Answer:

115/12

HOPE IT IS THE ANS

Given tangent, ZN, to the circle and the arc [tex]\widehat{ZMB}[/tex] = 280°, we have that

the angle formed by the chord BZ and the tangent ZN, ∠BZN is 50°

The given parameters are;

A tangent to the circle O = ZN

[tex]m \widehat{ZMB}} = \mathbf{280^{\circ}}[/tex]

Required:

Angle ∠BZN

Solution;

Please find attached the drawing of the circle and tangent

From the drawing, we have;

∠BOZ = 360° - 280° = 80°

ΔBOZ is an isosceles triangle, which gives;

∠BZO = ∠ZBO

[tex]\angle BZO = \dfrac{(180^{\circ}- 80^{\circ}) }{2} = \mathbf{50^{\circ}}[/tex]

∠OZN = 90° (by definition of a tangent)

∠OZN = ∠BZO + ∠BZN

∠BZN = ∠OZN - ∠BZO

Which gives;

∠BZN = 90° - 40° = 50°

Learn more about tangents to a circle here:

https://brainly.com/question/14561226

Answer:

Step-by-step explanation:

total surface area = 584 m2

lateral surface area = 504 m2

top surface area = 40 m2

bottom surface area = 40 m2

Answer:

The amount per pound would be:
$2.40

Step-by-step explanation:

720 divided by 3 = 240
We can then conclude that:
$7.20 divided by 3 = $2.40


Have a great rest of your day
#TheWizzer

Answer:

0.15 dollars, of 15 cents (I believe)

Step-by-step explanation:

3 pounds, 16 oz per pound is 48 oz. 7.20 divided by 48 oz is 0.15, which should be equal to 15 cents. Hope this helps :)

Answer:

32.202

Step-by-step explanation:

Answer:

5 times a number subtracted from another number divided by 3.

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

for one cup 28/12

for 18 cup,

(28/12)×18

=42

Answer:

The dimensions on paper are 1.992ft by 5.976ft with a scale factor of 7.53

Step-by-step explanation:

The first step will be to find the diagonal of the rea life mural.

We can use Pythagoras' Theorem to do this.

Diagonal = [tex]\sqrt{15^2 +45^2 }[/tex] =47.43 feet.

Now we have the real-life diagonal, we will now relate the diagonal of the painting outside with the one on paper. We can do this by dividing the two diagonals.

This will be 47.43 / 6.3 units = 7.53.

The scale factor is 7.53

To get the dimensions of the length and the breadth on paper, we divide the outside dimensions by the scale factor.

This will be

Length = 15/ 7.53 = 1.992

Breadth = 45/7.53 = 5.976

Therefore, the dimensions on paper are 1.992ft by 5.976ft with a scale factor of 7.53

Answer:

Q1: No solutions

Q2: x=2, y=-2

Q3: x=1, y=4

Step-by-step explanation:

Q1: Found out 0y = 18 which is impossible therefore no solution.

Q2:

In the first equation: [tex]2x - 4y = 12[/tex]

Let's express x in terms of y by changing the subject. Follow my steps.

[tex]2x = 12+4y[/tex]

[tex]x = \frac{12+4y}{2}[/tex]

Now let's put the x above into the second equation: [tex]-14x-4y=-20[/tex]

It becomes: [tex]-14(\frac{12+4y}{2})-4y=-20[/tex]. Follow my steps.

[tex]-7(12+4y)=-20+4y[/tex]

[tex]-84-28y=-20+4y[/tex]

[tex]-32y=64[/tex]

[tex]y=-2[/tex]

Put y = -2 into the first equation:

[tex]2x-4(-2)=12[/tex]

[tex]2x+8=12[/tex]

[tex]2x=12-8[/tex]

[tex]2x=4[/tex]

[tex]x=2[/tex]

Q3:

Multiply the first equation by 3 and the second equation by 7, so that both are 21x.

1st equation:
[tex]3(7x-3y)=3(-5)[/tex]
[tex]21x-9y=-15[/tex]

2nd equation:

[tex]7(3x+2y) = 7(11)[/tex]

[tex]21x+14y = 77[/tex]

We can now substract the 2nd equation with the 1st equation so that both 21x cancels out and only the variable y remains.

[tex]21x-9y-(21x+14y)=-15-77[/tex]

[tex]21x-9y-21x-14y=-92[/tex]

[tex]-23y=-92[/tex]

[tex]y=4[/tex]

Put y = 4 into the second equation to find x.

[tex]3x+2(4)=11[/tex]

[tex]3x+8=11[/tex]

[tex]3x=11-8[/tex]

[tex]3x = 3[/tex]

[tex]x=1[/tex]

Answer:

3 pounds and 8 ounces

Step-by-step explanation:

1 pound is 16 ounces, 1/2 pound is 8 ounces.

If you need further help, let me know!

-profparis

Answer:

So a batch is 5/8

There are THREE 3/4th cups of flour in the cupboard.

So 3 three fourths so basically
3/4 * 3 = 9/4 or

3/4 + 3/4 + 3/4 = 9/4

9/4 and each batch is 5/8.
9/4 ÷ 5/8 = 72/20 or 3 1/10

3 batches of cookies.

Answer:

Step-by-step explanation:

Factorize

Answer: x=10

Step-by-step explanation: A straight line is equal to 180 degrees, meaning that the sum of all angles is supplementary to 180 degrees. This can be written as 3x+88+x+36+2x-4=180. Adding like terms, it is simplified to 6x+120=180. Subtract 120 on both sides getting you 6x=60. Then divide; x=10

Answer

The anwser is B

Step-by-step explanation:

I did this test as well earlier this year

Equation x=3 represents a line perpendicular to the x-axis. Therefore, the correct answer is option A.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

here, we have,

A) x=3

Graph the line using the slope and y-intercept, or two points.

Slope: Undefined

y-intercept: No y-intercept

The coordinate points are (3, 0) and (3, 1).

B) Graph the line using the slope and y-intercept, or two points.

Slope: 1

y-intercept: (0,0)

The coordinate points are (0, 0) and (1, 1)

C) x=y

Graph the line using the slope and y-intercept, or two points.

Slope: 1

y-intercept: (0,0)

The coordinate points are (0, 0) and (1, 1)

D) x=-3y

Graph the line using the slope and y-intercept, or two points.

Slope: -1/3

y-intercept: (0,0)

The coordinate points are (0, 0) and (-3, 1)

Therefore, option A is the correct answer.

To learn more about the the equation of a line visit:

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#SPJ7

Answer:

Step-by-step explanation:

When you list the trigonometic ratios for both acute angles in a right triangle, you notice some interesting developments.

Let's concentrate on sine and cosine:

Observation from the table above: notice1

In a right triangle, the sine of one acute angle, A, equals the cosine of the other acute angle, B.

If ∠A and ∠B are the acute angles of a right triangle,

sin A = cos B

Since the measures of these acute angles of a right triangle add to 90º, we know these acute angles are complementary. ∠A is the complement of ∠B, and ∠B is the complement of ∠A.

If we write, m∠B = 90º - m∠A    (or m∠A = 90º - m∠B ), and we substitute into the original observation, we have:

      notice4

If θ is substituted for m∠A , we establish the following relationship between sine and cosine:

sincosrule

The sine of any acute angle is equal to the cosine of its complement.

The cosine of any acute angle is equal to the sine of its complement.

Sine and cosine are called "cofunctions", where the sine (or cosine) function

of any acute angle equals its cofunction of the angle's complement.

FYI: What about tangent?

Yes, there is a "relationship" regarding the tangent of the two acute angles (A and B) in a right triangle. It is not, however, the same type of relationship that exists between sine and cosine.

The tangent of ∠A is the reciprocal (flip over) of the tangent of ∠B.

The angles being used in the following examples are acute angles.

ex1

If sin 30º = ½ and cos θ = ½,

find θ.  Solution: Since both trig functions = ½,

30º and θ must be complementary.

θ = 60º

ex2

If sin(3x + 10)º = cos(x + 24)º,

find x.  Solution: In order for the sine and cosine to be equal, the angles must be complementary.

3x + 10 + x + 24 = 90

4x + 34 = 90

4x = 56

x = 14

ex3

If sin(15º) = 0.26 and

cos (15º) = 0.97,

find sin(75º) and the cos(75º).  Solution: The sine of an angle and the cosine of its complement are equal.

15º and 75º are complementary.

sin(75º) = cos(15º) = 0.97

cos(75º) = sin(15º) = 0.26

ex4

In right ΔABC, m∠C = 90º,

sin A = x + 0.1 and cos B = 2x - 0.4. Find x.  Solution: If A and B are the acute angles of a right triangle, sin A = cos B.

x + 0.1 = 2x - 0.4

0.5 = x